Cooperman told CNBC the Wells Notice centers on trading of Atlas Pipeline — a stock they had owned for years, but no longer hold — since 2007. He held a conference call with Omega investors late Monday afternoon, where, according to those on the call, he said the investigation won't have a meaningful impact in firm's ability to serve its investors.

Those sources also told CNBC that Cooperman said his lawyers will vigorously fight any charges, and that the Wells notice also concerns untimely SEC filings in a handful of companies — he called that "piling on."

Katie Kramer | CNBC

Leon Cooperman, Chairman and CEO of Omega Advisors.

Cooperman told investors he and his lawyers will respond to the SEC by the end of the month, and that he offered to meet with its enforcement staff a year ago, but they refused, those on the call said. The fund manager also said his firm "can definitively prove we've done nothing wrong," and he's "not going to let the SEC change his reputation," CNBC learned.

The investor also said there was no pattern of insider trading, and he believed the matter would be resolved favorably, those on the call said.

According to a report from Dow Jones, Cooperman cited his Fifth Amendment rights in declining to testify after receiving a subpoena. He wrote in the letter that "we strongly disagree...that any violation of federal securities laws has occurred," Dow Jones reported.

A Wells notice is a letter sent by a regulator notifying the recipient that the agency intends to pursue an enforcement action against them.

Cooperman said in a letter last year that his firm had been subpoenaed by the U.S. Attorney's Office in New Jersey and the SEC regarding the trading of certain securities.